Linearization of analytic order relations
Abstract
We prove that if $\leq$ is an analytic partial order then either $\leq$ can be extended to a (boldface) $\Delta^1_2$ linear order similar to an antichain in $2^{<\omega_1}$ ordered lexicographically or a certain Borel partial order $\leq_0$ embeds in $\leq.$ Some corollaries for analytic equivalence relations are given, for instance, if $E$ is a $\Sigma^1_1[z]$ equivalence relation such that $E_0$ does not embed in $E$ then $E$ is determined by intersections with Einvariand Borel sets coded in $L[z]$.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 1997
 DOI:
 10.48550/arXiv.math/9706204
 arXiv:
 arXiv:math/9706204
 Bibcode:
 1997math......6204K
 Keywords:

 Mathematics  Logic
 EPrint:
 Annals of Pure and Applied Logic, 2000, 102, 12, pp. 69100